Connection timeout is incorrectly reported as invalid token #8293

Describe the bug

Connect timeout is incorrectly reported as invalid token

Steps to reproduce the behavior

1. Authenticate to a GHE host (eg: ghe.mycorp.org) on the VPN, then disconnect from the VPN
2. Note that the connection now times out, eg:

   ❯ curl --connect-timeout 5 https://ghe.mycorp.org
   curl: (28) Failed to connect to ghe.mycorp.org port 443 after 2005 ms: Timeout was reached
   

3. Check auth status, eg:

   ❯ gh auth status -h ghe.mycorp.org
   ghe.mycorp.org
     X ghe.mycorp.org: authentication failed
     - The ghe.mycorp.org token in keyring is invalid.
     - To re-authenticate, run: gh auth login -h ghe.mycorp.org
     - To forget about this host, run: gh auth logout -h ghe.mycorp.org    
   

Expected vs actual behavior

Connection timeouts should be reported as connection timeout rather than an invalid token. An invalid token suggests reauthentication is required, when the solution is to resolve the connection timeout (eg: by connecting to the VPN).

Logs

❯ gh --version
gh version 2.38.0 (2023-11-01)
https://github.com/cli/cli/releases/tag/v2.38.0